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A Relaxed Projection Method for Split Variational Inequalities

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Abstract

We study the recently introduced split variational inequality under the framework of variational inequalities in a product space. The feature of our equivalent formulation of split variational inequality is its variable separability (that is, splitting nature) together with a linear constraint. We propose a relaxed projection method, which fully exploits the splitting structure of split variational inequality and which is not only easily implementable, but also globally convergent under some mild conditions. Our numerical results on finding the minimum-norm solution of the split feasibility problem and on solving a separable and convex quadratic programming problem verify the efficiency and stability of our new method.

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Acknowledgments

The authors were grateful to the two anonymous referees for their valuable comments and suggestions which improved the presentation of the paper. The first two authors were supported by NSFC (11171083, 11301123), Zhangjiang Provincial NSFC LZ14A010003 and Research Foundation of Hangzhou Dianzi University (KYS075612037). The third author was supported in part by NSC 102-2115-M-110-001-MY3.

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Authors and Affiliations

  1. Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, 310018, China

    Hongjin He & Chen Ling

  2. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, 80424, Taiwan

    Hong-Kun Xu

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  1. Hongjin He
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  2. Chen Ling
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Correspondence to Hong-Kun Xu.

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He, H., Ling, C. & Xu, HK. A Relaxed Projection Method for Split Variational Inequalities. J Optim Theory Appl 166, 213–233 (2015). https://doi.org/10.1007/s10957-014-0598-3

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